arXiv:2507. 07008v2 Announce Type: replace Abstract: Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature.
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling (SGS) with Langevin dynamics for the likelihood step and Stochastic Interpolants (SI) for the prior step. By integrating a pretrained flow model into the prior step via SI's reverse-time SDE and a novel timestep correction, FlowSGS reduces the number of network evaluations compared to plug‑and‑play diffusion samplers. Experiments demonstrate state‑of‑the‑art performance on various inverse problems, including the first flow‑based solution to a nonlinear inverse problem (Fourier phase retrieval).
arXiv:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
The paper introduces LUD-DIF, a diffusion-based method that solves inverse problems using unpaired data. By deriving the evidence lower bound of the joint distribution and decoupling it into two independent diffusion processes under a weak‑coupling assumption, the authors provide a variational inference framework, a loss function, and an error‑bound analysis. Experiments show that LUD‑DIF performs well across multiple image inverse problems, demonstrating its effectiveness and generalization in unpaired settings.
arXiv:2609.37529v1 Announce Type: cross Abstract: Pretrained denoisers provide a powerful way to incorporate image priors into restoration algorithms. Plug-and-Play and RED approaches exploit fixed-n...
Score‑based diffusion models excel at inverse problems but suffer from slow inference and task‑specific hyperparameter tuning. This paper introduces principled reparameterizations that create invariances, enabling the reuse of the same hyperparameters across different tasks. Building on the RED‑diff framework, the authors present OptDiff, a streamlined pipeline that integrates convex optimization to accelerate inference, achieving notable speedups and higher image quality in reconstruction, deblurring, and super‑resolution experiments.
The paper investigates stochastic inverse problems where the goal is to recover a probability distribution of an unknown parameter that explains observed data. It examines direct inversion, a variational formulation with regularization, and optimization via Wasserstein gradient flows, highlighting parallels and differences with deterministic inverse problems. A key finding is that the choice of metric—both in the loss function and during optimization—strongly influences stability and the optimizer’s properties.
arXiv:2602. 11059v2 Announce Type: replace-cross Abstract: This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive error, (2) the problem is ill-posed and regularization relies on a Bayesian strategy, (3)~the prior is modeled by a diffusion process adjusted on an available large set of examples.
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
arXiv:2609.14596v1 Announce Type: new Abstract: Training-free diffusion inverse solvers typically choose between local measurement guidance and costly clean-space posterior updates. Independent poste...